ancient Oriental and Greco-Roman deity, known by a variety of local names; the name Cybele or Cybebe predominates in Greek and Roman literature from about the 5th century bc onward. Her full official Roman name was Mater Deum Magna Idaea (Great Idaean Mother of the Gods)....

...and by the Second Vatican Council, commonly referred to as Vatican II. During his brief reign, Pope John issued several important encyclicals. Of special interest is Mater et magistra (“Mother and Teacher”), published on May 15, 1961, which explicitly aligned itself with Rerum novarum of Leo XIII in calling for......

in Roman religion, goddess of the ripening of grain (although the Latin poet Lucretius made her a goddess of dawn). Her worship in Italy was widespread and of ancient origin. Her temple at Rome, located in the Forum Boarium, was discovered under the Church of St. Omobono in 1937. The oldest sanctuary there was built in the 7th century bc. A small temple, first built earlier in the 6t...

...health ambulance service. There are several private ambulance services, including air ambulances. Dublin contains numerous public and private hospitals, including four university hospitals—the Mater Misericordiae, Beaumont, St. Vincent’s, and St. James’s. All have departments of international repute ranging from children’s care to transplants and diagnostics. The Mat...

city, Basilicata regione, southern Italy. It lies above a deep ravine northwest of Taranto. Of obscure origin, the town formed part of the duchy of Benevento and of the principality of Salerno and was occupied successively by the Normans, the Aragonese, and the Orsini. In the old part of the city on the slope of the ravine, people historically inhabited cavelike houses cu...

...not only the form but also the “species” of an object is in the intellect. A species is a combination of form and something like a general idea of matter, which Aquinas called “common matter.” Common matter is contrasted with “individuated matter,” which is the stuff that comprises the physical bulk of an object. One objection to this theory is that it....

...Goals of the Scholar”; also known as Picatrix) and Rutbat al-ḥakīm (“The Step of the Scholar”). Greater interest is merited by the Materia medica, a revision of the Eastern Arabic text of the 1st-century Greek physician Pedanius Dioscorides ordered by al-Naṣir, on which Jews, Arabs, and Christians collaborated.......

the study of the properties of solid materials and how those properties are determined by a material’s composition and structure. It grew out of an amalgam of solid-state physics, metallurgy, and chemistry, since the rich variety of materials properties cannot be understood within the context of any single classical discipline. With a basic understanding of the origins of properties, materi...

...goods. Foreign trade also had to be taken into account, as a drain on available resources (exports) and as a source of needed goods (imports). The planners proceeded by drawing up a series of material balances, which expressed anticipated supply of, and demand for, all key commodities. The successive versions of the plan were revised until a general balance was attained, since it was no......

Treaties may be terminated or suspended through a provision in the treaty (if one exists) or by the consent of the parties. In the case of a material breach—i.e., an impermissible repudiation of the treaty or a violation of a provision essential to the treaty’s object or purpose—the innocent party of a bilateral treaty may invoke that breach as a ground for terminating the tre...

...places Aristotle distinguishes four types of cause, or explanation. First, he says, there is that of which and out of which a thing is made, such as the bronze of a statue. This is called the material cause. Second, there is the form or pattern of a thing, which may be expressed in its definition; Aristotle’s example is the proportion of the length of two strings in a lyre, which is the....

All of the nomads so far mentioned share important general characteristics. The first and most obvious is that their nomadism severely restricts the amount of their “baggage,” or material culture. Bows and arrows (except in Australia, where the unique boomerang is used instead) and perhaps a simple spear javelin, or in some areas throwing sticks or clubs, are the usual hunting and......

Other important causes of signal distortion in optical fibres are material dispersion and waveguide dispersion. Material dispersion is a phenomenon in which different optical wavelengths propagate at different velocities, depending on the refractive index of the material used in the fibre core. Waveguide dispersion depends not on the material of the fibre core but on its diameter; it too causes......

in logic and mathematics, the formation of a proposition from two others which are linked by the phrase “if, and only if.” The equivalence formed from two propositions p and q also may be defined by the statement “p is a necessary and sufficient condition for q.”...

...arguments (p, q) are known as disjuncts.Given any two propositions p and q, then p ⊃ q (“if p [then] q” or “p [materially] implies q”) is to count as false when p is true and q is false and as true in all other cases; hence it has the same meaning as “either not-p...

...every referent (x); it is disparate if it fails to characterize some or all of the referents. The predication is formal if the subject necessarily entails (or excludes) the predicate; it is material if the entailment is contingent....

...or financial intermediaries, typically enter into longer-term commitments with the producer and make up what is known as the marketing channel, or the channel of distribution. Manufacturers use raw materials to produce finished products, which in turn may be sent directly to the retailer, or, less often, to the consumer. However, as a general rule, finished goods flow from the manufacturer......

Actual sin is also subdivided into material and formal. Formal sin is both wrong in itself and known by the sinner to be wrong; it therefore involves him in personal guilt. Material sin consists of an act that is wrong in itself (because contrary to God’s law and human moral nature) but which the sinner does not know to be wrong and for which he is therefore not personally culpable....

...on the author), three main types of supposition were distinguished: (1) personal supposition (which, despite the name, need not have anything to do with persons), (2) simple supposition, and (3) material supposition. These types are illustrated, respectively, by the occurrences of the term horse in the statements “Every horse is an animal” (in which the term horse......

...Democracy in the Democratic Revolution. He fiercely attacked the influence of Kantian philosophy on German and Russian Marxism in Materializm i empiriokrititsizm (1908; Materialism and Empirio-criticism (1908). In 1912 at the Prague Conference the Bolsheviks constituted themselves as an independent party. During World War I Lenin resided in Switzerland, wh...

...precognition) but the more complex phenomenon of spirit contact. By the end of the 19th century, significant efforts were being made to verify the phenomena of mediumship, especially the occasional materialization of spirit entities. Many who participated in psychic research hoped for positive results and occasionally concluded that they had proved the existence of clairvoyance or established.....

...and daughter of the emperor. In 1118 the empress Irene and Anna tried unsuccessfully to have him named successor to Alexius I. At the suggestion of his mother-in-law, he wrote the chronicle (“Materials for a History”) of the Comnenus family in the 11th century, particularly during the years 1070–79. In addition to information derived from older contemporaries such as his......

the movement of raw goods from their native site to the point of use in manufacturing, their subsequent manipulation in production processes, and the transfer of finished products from factories and their distribution to users or sales outlets....

the series of operations that transforms industrial materials from a raw-material state into finished parts or products. Industrial materials are defined as those used in the manufacture of “hard” goods, such as more or less durable machines and equipment produced for industry and consumers, as contrasted with disposable “soft” goods, such as chemicals, foodstuffs, pha...

solid-waste management plant that processes recyclable materials to sell to manufacturers as raw materials for new products. MRFs are generally classified as either “clean” or “dirty,” depending on whether the facility handles materials that are mixed with other municipal waste. MRFs play an important role in reducing the waste stream, the demand for ...

solid-waste management plant that processes recyclable materials to sell to manufacturers as raw materials for new products. MRFs are generally classified as either “clean” or “dirty,” depending on whether the facility handles materials that are mixed with other municipal waste. MRFs play an important role in reducing the waste stream, the demand for ...

solid-waste management plant that processes recyclable materials to sell to manufacturers as raw materials for new products. MRFs are generally classified as either “clean” or “dirty,” depending on whether the facility handles materials that are mixed with other municipal waste. MRFs play an important role in reducing the waste stream, the demand for ...

recovery and reprocessing of waste materials for use in new products. The basic phases in recycling are the collection of waste materials, their processing or manufacture into new products, and the purchase of those products, which may then themselves be recycled. Typical materials that are recycled include iron and steel scrap, alu...

the study of the properties of solid materials and how those properties are determined by a material’s composition and structure. It grew out of an amalgam of solid-state physics, metallurgy, and chemistry, since the rich variety of materials properties cannot be understood within the context of any single classical discipline. With a basic understanding of the origins of...

measurement of the characteristics and behaviour of such substances as metals, ceramics, or plastics under various conditions. The data thus obtained can be used in specifying the suitability of materials for various applications—e.g., building or aircraft construction, machinery, or packaging. A full- or small-scale model of a proposed machine or structure may be tested. Alternative...

The transmission of genes that are located in mitochondria (i.e., not contained in the nucleus of the cell) is termed maternal (mitochondrial) inheritance. Mitochondrial DNA (mtDNA), although much smaller than nuclear DNA, is critical in cellular metabolism. Most of the energy required by a cell to drive its metabolism is produced in mitochondria by proteins in a series of electron......

a French school for children between two and six years old. Private schools for young children were founded in France around 1779, under the influence of Jean-Jacques Rousseau’s Émile. The central government took over most of them in 1833 and named them maternal schools, hoping that the care would be like that of a mother. Pauline Kergomard, general inspecto...

...Genetic imprinting involves a sex-specific process of chemical modification to the imprinted genes, so that they are expressed unequally, depending on the sex of the parent of origin. So-called maternally imprinted genes are generally expressed only when inherited from the father, and so-called paternally imprinted genes are generally expressed only when inherited from the mother. The......

The nutritional status of the mother is important throughout this period. The Food and Nutrition Board of the National Research Council recommends a daily caloric increase of approximately 400 kilocalories over nonpregnant diet. Most drugs that are taken during this time are secreted through the milk, and smoking reduces breast-milk volume and decreases infant growth rates....

During the first half of the 20th century in the United Kingdom, the emphasis shifted gradually from environmental toward personal public health. A succession of statutes, of which the Maternity and Child Welfare Act (1918) was probably the most important, placed responsibility for most of the work on county governments. National health insurance (1911) gave benefits to 16 million workers and......

The most common species, valued for their unusual foliage, include the panda plant (Kalanchoe tomentosa); penwiper plant (K. marmorata); air plant, or maternity plant (K. pinnata); velvet leaf, or felt bush (K. beharensis); devil’s backbone (K. daigremontiana); and South American air plant (K. fedtschenkoi). A range of attractive potted plants......

...extent, skepticism is born of such reflection. Some ancient skeptics contended that all arguments are equally bad and, accordingly, that nothing can be proved. The contemporary American philosopher Benson Mates, who claims to be a modern representative of this tradition, has argued that all philosophical arguments are equally good....

...Romantic sensibility in extraordinary fragments of lyrical intensity, which gave a new prestige to the Demotic language. Solomós’ followers continued to cultivate the Demotic, particularly Antónios Mátesis, whose historical social drama, O vasilikós (1859; “The Basil Plant”), was the first prose work of any length to be written in the Demo...

...(1928–29; “Black Wings”), which examines social problems in Poland’s coal-mining regions, Generał Barcz (1922–23; “General Barcz”), and Mateusz Bigda (1933; “Matthew Bigda”). The latter two satirically describe political life after Poland regained independence. Considered by many critics to offer car...

His films as a director include Lianna (1983); Baby, It’s You (1983); Matewan (1987), a drama about coal miners fighting to form a union in the 1920s; The Brother from Another Planet (1984), a science-fiction comedy that lacerates discrimination; City of Hope (1991); ......

in the Welsh collection of stories known as the Mabinogion, king of Gwynedd in the North. He is also the brother of Dôn, who is probably the Welsh counterpart of the Irish goddess Danu. Whenever at peace, it was necessary for Math to have his feet upon a virgin’s lap. The virgin who held Math’s feet was raped by one of h...

the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the ph...

...adventures of two of the escapees, Manawydan (Brân and Branwen’s brother) and Pryderi, who with his wife, Cigfa, and mother, Rhiannon, combat an enchantment placed over Pryderi’s realm. Math fab Mathonwy (“Math Son of Mathonwy”) is a complex tale focusing on Math, a prince of northern Wales, his nephew Gwydion, and Gwydion’s nephew Lleu Llaw Gyff...

in Hinduism, any monastic establishment of world renouncers or sannyasis. The first mathas were founded by the great teacher Shankara in the 8th century ce. Shankara was said to have established four mathas...

...lettres came to occupy in the life of the court and its patronage system was reflected in a later work of compilation, Ḍiyāʾ al-Dīn ibn al-Athīr’s Al-Mathal al-sāʾir fī adab al-kātib wa al-shāʿir (“The Current Model for the Literary Discipline of the Scribe and Poet”), wher...

...languages has found wide commercial acceptance. On the other hand, high-level user-interface languages for special-purpose software have been much more successful; for example, languages like Mathematica, in which sophisticated mathematics may be easily expressed, or the “fourth generation” database-querying languages that allow users to express requests for data with simple......

Boole published two major works, The Mathematical Analysis of Logic in 1847 and An Investigation of the Laws of Thought in 1854. It was the first of these two works that had the deeper impact on his contemporaries and on the history of logic. The Mathematical Analysis of Logic arose as the result of two broad streams of influence. The first was the English......

Xenakis’s long and fruitful association with the Paris Instrumental Ensemble for Contemporary Music led to frequent performances and recordings of his works for chamber ensemble. He established the School of Mathematical and Automatic Music in 1966. Other works by Xenakis include Polla ta dhina for children’s chorus and orchestra (1962), ......

Many philosophers cannot bring themselves to believe in abstract objects. However, there are not many tenable alternatives to mathematical Platonism. One option is to maintain that there do exist such things as numbers and sets (and that mathematical theorems provide true descriptions of these things) while denying that these things are abstract objects. Views of this kind can be called......

Computational biology is more easily distinguished from mathematical biology, though there are overlaps. The older discipline of mathematical biology was concerned primarily with applications of numerical analysis, especially differential equations, to topics such as population dynamics and enzyme kinetics. It later expanded to include the application of advanced mathematical approaches in......

Descartes’s goal in La Géométrie was to achieve the construction of solutions to geometric problems by means of instruments that were acceptable generalizations of ruler and compass. Algebra was a tool to be used in this program:If, then, we wish to solve any problem, we first suppose the solution already effected, and give names to all the lines that ...

Given a random variable X with distribution f, the expected value of X, denoted E(X), is defined by E(X) = ∑ixif(xi). In words, the expected value of X is the sum of each of the possible values of X multiplied by the probability of obtaining...

...(“private lecturer”) at the Universities of Berlin (1927–29) and Hamburg (1929–30). The work with Hilbert culminated in von Neumann’s book The Mathematical Foundations of Quantum Mechanics (1932), in which quantum states are treated as vectors in a Hilbert space. This mathematical synthesis reconciled the seemingly contradictory......

3. Rule of inference (the principle of mathematical induction): If zero has some property p and it is the case that if any number has p then its successor does, then every number has p. With some of the notation from above, this can be expressed: If A(0) and (∀x)(∼A(x) ∨ A(Sx)) are theorems, then......

What is commonly referred to as mathematical linguistics comprises two areas of research: the study of the statistical structure of texts and the construction of mathematical models of the phonological and grammatical structure of languages. These two branches of mathematical linguistics, which may be termed statistical and algebraic linguistics, respectively, are typically distinct. Attempts......

the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and t...

either a physical representation of mathematical concepts or a mathematical representation of reality. Physical mathematical models include reproductions of plane and solid geometric figures made of cardboard, wood, plastic, or other substances; models of conic sections, curves in space, or three-dimensional surfaces of various kinds made of wire, plaster, or thread strung from ...

Nominalism is the view that mathematical objects such as numbers and sets and circles do not really exist. Nominalists do admit that there are such things as piles of three eggs and ideas of the number 3 in people’s heads, but they do not think that any of these things is the number 3. Of course, when nominalists deny that the number 3 is a physical or mental object, they are in agreement w...

...a short tract entitled De Motu (“On Motion”). Already Newton was at work improving and expanding it. In two and a half years, the tract De Motu grew into Philosophiae Naturalis Principia Mathematica, which is not only Newton’s masterpiece but also the fundamental work for the whole of modern science....

theoretical tool of management science and economics in which management operations are described by mathematical equations that can be manipulated for a variety of purposes. If the basic descriptions involved take the form of linear algebraic equations, the technique is described as linear programming. If more complex forms are required, the term non...

Concept of the adequacy of a formal system that is employed both in proof theory and in model theory (see logic). In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in the system is such that either it or its negation is provable in the system. In model theory, a formal system is said to be semantically complete if and only if every......

...depended so heavily on mathematical techniques—especially the calculus of variations—that the book may have deterred otherwise interested readers. His most famous work, Mathematical Psychics (1881), presented his new ideas on the generalized utility function, the indifference curve, and the contract curve, all of which have become standard devices of econo...

...contributor to the Strand Magazine, published several very popular collections of puzzles that have been reprinted from time to time (1917–67). The first edition of W.W. Rouse Ball’s Mathematical Recreations and Essays appeared in 1892; it soon became a classic, largely because of its scholarly approach. After passing through 10 editions it was revised by the British...

The real birth of modern information theory can be traced to the publication in 1948 of Claude Shannon’s “A Mathematical Theory of Communication” in the Bell System Technical Journal. A key step in Shannon’s work was his realization that, in order to have a theory, communication signals must be treated in isolation from the meaning of the messages that they trans...

...to analysis and partial differential equations, Copson wrote the widely used Introduction to the Theory of Functions of a Complex Variable (1935) and, in collaboration with Bevan B. Baker, The Mathematical Theory of Huygens’ Principle (1939), concerning the generation and structure of waves. His other publications include Asymptotic Expansions (1965) and Metric Sp...

...English language. His Report on the Relativity Theory of Gravitation (1918), written for the Physical Society, followed by Space, Time and Gravitation (1920) and his great treatise The Mathematical Theory of Relativity (1923)—the latter considered by Einstein the finest presentation of the subject in any language—made Eddington a leader in the field of......

...(now the University of Manchester). Lamb wrote the A Treatise on the Mathematical Theory of the Motion of Fluids (1879), which was enlarged and transformed into Hydrodynamics (1895); the latter was for many years the standard work on hydrodynamics. His other publications include Infinitesimal Calculus (1897), Dynamical Theory of......

...into two main sects, later called akousmatikoi (from akousma, viz., the esoteric teachings) and mathēmatikoi (from mathēmatikos, “scientific”), may have occurred at that time. The acousmatics devoted themselves to the...

...Inequalities (1934) with Littlewood, The Theory of Numbers (1938) with E.M. Wright, and Divergent Series (1948). A Mathematician’s Apology (1940), which gives a completely personal account of how mathematicians think, continues to be widely read. He was widely honoured for his work, being elected a......

the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy. Mathematicism is manifested in Western philosophy in at least three ways: (1) General mathematical methods of investigation can be used to establish consistency of meaning and completeness of analysis. This is the revolutionary approach introduced in the first ...

Hull’s learning theories were first presented in Mathematico-Deductive Theory of Rote Learning (1940), a collaboration with several coworkers, in which he expressed his findings through postulates stated in both mathematical and verbal forms. Hull believed that psychology had its own quantitative laws that could be stated in mathematical equations. He further developed these i...

the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the ph...

The brakeman-fireman-engineer puzzle has become a classic. The following version of it appeared in Oswald Jacoby and William Benson’s Mathematics for Pleasure (1962).The names, not necessarily respectively, of the brakeman, fireman, and engineer of a certain train were Smith, Jones, and Robinson. Three passengers on the train happened to have the same names and, in order ...

the study of the logical and philosophical basis of mathematics, including whether the axioms of a given system ensure its completeness and its consistency. Because mathematics has served as a model for rational inquiry in the West and is used extensively in the sciences, foundational studies have far-reaching consequences for the reliability and extensibility...

branch of philosophy that is concerned with two major questions: one concerning the meanings of ordinary mathematical sentences and the other concerning the issue of whether abstract objects exist. The first is a straightforward question of interpretation: What is the best way to interpret standard mathematical sentences and theories? In other words, what is really meant by ordinary mathematical s...

Bell is best known for his popular books, such as Men of Mathematics (1937) and Mathematics, Queen and Servant of Science (1951). He also wrote a history of Fermat’s last theorem, The Last Problem (1961). Although rather fanciful and not always historically accurate, these works, particularly Men of...

...into two main sects, later called akousmatikoi (from akousma, viz., the esoteric teachings) and mathēmatikoi (from mathēmatikos, “scientific”), may have occurred at that time. The acousmatics devoted themselves to the...

American Congregational minister and author, supporter of the old order of the ruling clergy, who became the most celebrated of all New England Puritans. He combined a mystical strain (he believed in the existence of witchcraft) with a modern scientific interest (he supported smallpox inoculation)....

Boston Congregational minister, author and educator, who was a determining influence in the councils of New England during the crucial period when leadership passed into the hands of the first native-born generation. He was the son of Richard Mather, son-in-law of John Cotton, and father of Cotton Mather....

English-born American Congregational minister, father of Increase Mather and three other Puritan ministers. After joining the Great Migration of Puritans from England to New England (1635), he was elected “teacher” minister at Dorchester, Mass., and became locally celebrated as a preacher and formulator of Congregational creed and policy....

hill station (resort town) in western Maharashtra state, west-central India. It is located at an elevation of about 2,625 feet (800 metres) on the western side of the Western Ghats range, about 28 miles (45 km) east of Mumbai (formerly Bombay)....

In 1657 Wallis published the Mathesis Universalis (“Universal Mathematics”), on algebra, arithmetic, and geometry, in which he further developed notation. He invented and introduced the symbol ∞ for infinity. This symbol found use in treating a series of squares of indivisibles. His introduction of negative and fractional exponential notation was an important advance......

Czech linguist and scholar of English language and literature. He was the founder (1926) and president of the Prague Linguistic Circle, famous for its influence on structural linguistics and for its phonological studies. Mathesius taught at Charles University in Prague, beginning in 1909 after he had received his degree in Germanic and Romance studies. He became its first professor of Anglistics i...